Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C31×C3⋊(C5⋊D5) #42124989
Order 27900.
352 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C31 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C22×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52×C31 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2×C3×C31 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C31×C3⋊(C5⋊D5) | 2 |
| C2×C32×C52×C31 | 2 |
| C2×C3×C31×C5⋊D5 | 3 |
| C2×C31×C3⋊(C5⋊D5) | 3 |
| C2×C3×D15×C31 | 5 |
| C2×C3×C3⋊(C5⋊D5) | 31 |